Question

An electron is confined in a harmonic oscillator potential well. What is the longest wavelength of light that the electron can absorb if the net force on the electron behaves as though it has a spring constant of 74 N/m? (m el = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, ℏ = 1.055 × 10-34 J · s, h = 6.626 × 10-34 J · s)

Answer 1

The longest wavelength of light is 209 nm.

Step-by-step explanation:

Given that,

Spring constant = 74 N/m

Mass of electron
`m= 9.11*10^(-31)\ kg`

Speed of light
`c= 3*10^(8)\ m/s`

We need to calculate the frequency

Using formula of frequency

`f =(1)/(2\pi)\sqrt{(k)/(m)}`

Where, k= spring constant

m = mass of the particle

Put the value into the formula

`f=(1)/(2\pi)\sqrt{(74)/(9.11*10^(-31))}`

`f=1.434*10^(15)\ Hz`

We need to calculate the longest wavelength that the electron can absorb

`\lambda=(c)/(f)`

Where, c = speed of light

f = frequency

Put the value into the formula

`\lambda =(3*10^(8))/(1.434*10^(15))`

`\lambda=2.092*10^(-7)\ m`

`\lambda=209\ nm`

Hence, The longest wavelength of light is 209 nm.